Wikipedia:

The Blu-ray [and] DVD was scanned as 4K resolution from three different 35mm prints and rectified the quality issues of the 2001 DVD

This article, which Wikipedia uses as a source, goes into more detail:

A little background: Digital video is mastered by putting a film through a machine that digitally scans each frame, storing the information as a stream of pixels. Later another machine translates these data back into an image. The higher number of pixels, the more detailed and truer is the image.

The digital master for the 2002 DVD of Citizen Kane was made from a "high-definition" scan—i.e., with a machine that scanned each frame as 1,080 lines horizontally and 1,920 vertically, or 2 million pixels in all.

For the new Blu-ray, the digital master was made from a "4K" scan—4,096 lines horizontally and 3,112 vertically, or more than 12 million pixels in all, per frame. That is to say, 4K scanning produces a raw image having six times the resolution of a high-def scan.

At the moment, no commercial TV monitor can display a 4K image, nor any commercially available disc-player read it. But when digital-mastering technicians work with a 4K scan on their equipment, they can manipulate the data—correct the color, adjust contrast, clean dirt, fill in missing information—in ultra-microscopic detail.

...

For the new Blu-ray, Ned Price and his team at Warner Brothers Motion Picture Imagery scanned three different copies (or "film elements"): the MoMA print; a 35 mm fine-grain master that was found several years ago at a film lab in Brussels; and another 35 mm fine-grain master, discovered much more recently at a European film archive. (For a purely technical caveat, click here.)

"The three film elements had different strengths and weaknesses," Price explained. "For instance, one of them had less flicker in one reel but coarser grain in another reel. So we put together the best bits and pieces of all three." (Even so, Price and his team had to clean up, frame by frame, a lot of dirt and misalignments, especially in all those opticals and dissolves. The restoration project took over a year to complete.)

P.S: I don't think jaiy0 should be downvoted for their question, even if it might sound naive. On the contrary, people honestly asking questions should be upvoted for their curiosity :-)

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I can't speak for this movie specifically, but it was probably done the same way any film movie is remastered at 1080p, they take the film and simply rescan it.

Note, this is why certain TV shows don't get an HD update, because a lot of shows, while shot on film, were edited and had the masters on tape. This is why Star Trek TNG is remastered for Blu-Ray but the other shows are not, they had to go back and redo the whole process in order to rescan the footage. It's tedious and expensive. But for Citizen Kane, I imagine they just rescanned the film at a higher resolution. *

* note that I am just a random ass on the internet, don't take my half-ass explanation as gospel and I would love someone with more knowledge to step in. But that was my understanding.

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